This letter proposes structurally simple, bounded and partially bounded nonlinear controllers that offer satisfactory performance, demonstrated by their application to first and second-order dynamical systems. This is done by taking advantage of the properties of a particular class of bounded sector nonlinear functions that can be parameterized in bound value and slope. In contrast to the classical methods of saturated control, the proposed controllers’ design can be defined as an explicit summation of sector nonlinear functions, whose Lyapunov global stability proof can be straightforwardly demonstrated for the single and double integrator dynamics. Thus, the proposed approach derives nonlinear controllers where each term is bounded (or partially bounded) by design. Although the stability proof is provided for single and double integrator dynamics, one of the controllers is tested in a first-order nonlinear system and another in a nonlinear second-order system, both to achieve tracking. The numerical results evidence good performance even for large initial errors, and without the further introduction of auxiliary dynamics, such as compensation terms or feedback linearization. This is done by only tuning the gains of each term, while maintaining boundedness (or partial boundedness) properties on the control input.

This letter proposes an extension of the Extended Kalman Filter (EKF) for the state estimation of systems with unilateral constraints. The extension is a Unilateral Constrained Extended Kalman Filter (UCEKF) able to estimate the state of such systems conformed by continuous and discontinuous phases and a switching rule among them. In the continuous phase, the UCEKF is the EKF. In the discontinuous phase, when the constraint is active, the Differential Riccati Equation (DRE) solution of the UCEKF is deliberately modified to keep a quadratic Lyapunov function bounded. Such a function is quadratic in the estimation error and dependent on the DRE solution. The boundedness of such a function guarantees the boundedness of the estimation error at the discontinuous phase due to its nature. This function is also employed to prove the internal asymptotic convergence of the proposed UCEKF. The performance of both UCEKF and EKF is compared on a discontinuous Van der Pol oscillator state estimation task. Results confirm that the UCEKF outperforms the EKF in such state estimation.